The project is designed to develop new instrumentation and methods, and to improve existing instrumentation and techniques, for the characterization of biological macromolecules and the study of their interactions. Analytical ultracentrifugation, the techniques ancillary to it, and methods of data analysis using mathematical modeling appropriate for these techniques are the major areas of interest. Studies on the application of mathematical modeling to problems of ultracentrifugal analysis, and the development of new methods of performing experiments and analyzing data, have continued. In particular: (1) Extensive studies on the concentration dependence of sedimentation coefficients at very high protein concentrations have been continued. (2) Application of the method of implicit constraints to the analysis of simultaneous homogeneous and heterogeneous associations has been achieved. (3) A method has been developed for obtaining the upper and lower limits of the molecular weight of a glycoprotein when the composition of the carbohydrate portion is unknown. (4) A method has been developed for measuring the interaction of proteins with receptors having a heterogeneous molecular weight distribution. (5) A new method for the analysis of sedimentation velocity experiments has been developed.